Calcular algebras

DOI10.3318/PRIA.2019.119.05zbMath1501.47118arXiv1906.11959OpenAlexW2954071915MaRDI QIDQ5219091

John E. McCarthy, N. J. Young, Jim Agler

Publication date: 6 March 2020

Published in: Mathematical Proceedings of the Royal Irish Academy (Search for Journal in Brave)

Abstract: A calcular algebra is a subalgebra of $H^infty(Omega)$ with norm given by $| phi | = sup | phi(T) |$ as $T$ ranges over a given class of commutative $d$-tuples of operators with Taylor spectrum in $O$. We discuss what algebras arise this way, and how they can be represented.

Full work available at URL: https://arxiv.org/abs/1906.11959

zbMATH Keywords

Banach algebra holomorphic functions Taylor spectrum calcular algebra commuting $d$-tuples of operators

Mathematics Subject Classification ID

Abstract operator algebras on Hilbert spaces (47L30)

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